12 papers
Spanning -subdivisions with Prescribed Path Lengths
Zhilan Wang, Shuo Wei, Jin Yan
We study spanning -subdivisions in dense graphs where the length of every subdivision path is prescribed in advance. This problem is motivated in part by a question of Pavez-Sig…
Nearly balanced spanning subdivisions in dense digraphs
Zhilan Wang, Shuo Wei, Jin Yan
Pavez-Signé [Combin. Probab. Comput. 33 (2024), 121--128] conjectured a Dirac-type condition for spanning -subdivisions and asked whether the subdivision paths can additionally…
The exact total degree threshold for the square of a Hamilton cycle in digraphs
Zhilan Wang, Shuo Wei, Jin Yan
The Pósa-Seymour conjecture establishes the minimum degree threshold required to guarantee the presence of the th power of a Hamilton cycle in a graph. Following numerous partia…
Ramsey-Turán Type Problem for Perfect Transitive Triangle Tilings in Digraphs
Zhimin Wang, Zhilan Wang, Jin Yan
The classical Corrádi-Hajnal theorem states that for any multiple of , if is a graph with vertices and , then can be partitioned into verte…
Oriented Discrepancy of The Square of Hamilton Cycles
Yufei Chang, Yangyang Cheng, Zhilan Wang +2
For an oriented graph , the oriented discrepancy problem concerns the existence of a spanning subgraph of with a large imbalance between its forward and backward edge orient…
Spanning Subdivisions in Robustly Expanding Digraphs
Zhilan Wang, Jin Yan, Shuo Wei
Kühn, Osthus and Treglown [\emph{J. Combin. Theory Ser. B} \textbf{100} (2010)] proved that every sufficiently large robust outexpander with linear minimum semi-degree contains a H…
An Ore-type Theorem for Oriented Discrepancy of Hamilton Cycles
Yufei Chang, Yangyang Cheng, Zhilan Wang +2
Oriented discrepancy concerns the existence of prescribed subgraphs whose edges exhibit a substantial imbalance between the two directions. The Hamilton cycle case was first invest…
Spanning -subdivisions and perfect -subdivision tilings in dense digraphs
Yangyang Cheng, Zhilan Wang, Jin Yan
Given a (di)graph , we say that a (di)graph is an -subdivision if is obtained from by replacing one or more edges with internally vertex-disjoint pa…
A generalization of the Hamiltonian cycle in dense digraphs
Jie Zhang, Zhilan Wang, Jin Yan
Let D be a digraph and C be a cycle in D. For any two vertices x and y in D, the distance from x to y is the minimum length of a path from x to y. We denote the square of Let b…
Cycle-factors in oriented graphs
Zhilan Wang, Jin Yan, Jie Zhang
Let be a positive integer. A -cycle-factor of an oriented graph is a set of disjoint cycles of length that covers all vertices of the graph. In this paper, we prove that…
The generalizations of Hamiltonian in oriented graphs
Jia Zhou, Zhilan Wang, Jin Yan
An oriented graph is an orientation of a simple graph. In 2009, Keevash, Kühn and Osthus proved that every sufficiently large oriented graph of order with is Ham…
A Dirac-type theorem for arbitrary Hamiltonian -linked digraphs
Yangyang Cheng, Zhilan Wang, Jin Yan
Given any digraph on vertices, let be the family of all directed paths in , and let be a digraph with the arc set . The d…